All Questions

I see a lot of lecture notes where the terms "congruence" (ex: congruence relation) or deriving usages such as "the expression e is alpha-congruent to e2". Could someone please ...

It's known that there are different "kinds" of grammar complexity of language $L$ --- nonterminal complexity (minimal possible $|N|$ for grammar $(N, \Sigma, P, S)$ generating $L$), covering ...

tl;dr I'm trying to partition my students into groups with respect to their preferences, i.e. they can declare if they want to be with someone in a group or if they do not want to be with someone in a ...

Maximum independent set and minimum edge cover are a pair of related problems and are cover-packing problems. (Also see p114 of West's Introduction to Graph Theory) Are maximum independent set and ...

I am wondering if it can be shown that graph databases along with the graph database model and cypher queries are computationally equivalent to relational algebra. More specifically can cypher queries ...

Given array if numbers a[1..n]. Pair of numbers (i, j) is interesting, if i < j и a[i] > 2a[j]. How to count number of interesting pairs in O(nlogn)? What is the solution? My solution is not ...

I am sorry if this is not an advanced question. Most computer scientists believed that $Nexp \not \subset P/poly$ but they are not even close to this assumption. The main evidence that they are used ...

$FO^2$, i.e. two-variable first-order logic, has a NEXPTIME-complete satisfiability problem (see Grädel, Kolaitis and Vardi '97). However, the decidability and complexity of this fragment is proved by ...

Let us consider the following optimization problem. $\mathcal{P} =\{P_1,\cdots,P_n\}$, where $P_i\subset\mathbb{R}^d$. Let $m = max_i\lvert P_i\rvert$. The goal is to find a point $c$ such that ...

Given generator $g$ of a multiplicative group mod a prime $p$ the Diffie Hellman problem is to find $$g^{xy}\bmod p$$ from $g^x\bmod p$ and $g^y\bmod p$. The best way to solve this is through discrete ...

First let me describe the metric $k$-median problem. Definition (Metric $k$-Median): Given a set $C$ of clients and a set $L$ of facility locations defined over a distance metric $d$. Open a set $F$ ...

How is orthogonality implemented with Miranda, Haskell, Julia, Scheme, and Erlang languages?

I'm currently trying to find a reduction to this problem: Given a set S of n points (in the plane) in general position, is there a set of at least k triangles (formed using only points in S as ...

Let $G$ be a simple finite undirected graph. Let $\{V_1,V_2\}$ be a partition of its vertex set; that is, $V_1\cup V_2=V(G)$ and $V_1\cap V_2=\emptyset$. The partition $\{V_1,V_2\}$ is said to be an ...

Let ${\cal L}=\{Y_1,..., Y_k, X\}$ be a finite relational language such that $X$ is a unary relation name. Let $\phi(X,\bar{Y})\in{\cal L}$ be a first-order formula (the formula can have the equality ...

I'm trying to formalize the syntax and typing judgments of the Calculus of Constructions in Coq. I'm choosing to use the Pure Type Systems presentation of CoC; however, I've seen mild variations in ...

There are two sets $T$ and $M$. The set $T$ represents a set of tasks and the set $M$ consists of machines. A task $t_i \in T$ has two attributes: 1) a minimum-finish requirement $R_{t_i}$ and 2) an ...

We have a theoretical black box with no obvious inputs and outputs a value. For the sake of imagination, it's a literal black box with a digital counter on one side. We want to figure out what causes ...

A $k$-uniform hypergraph $H = (V, E)$ consists of a set of vertices $V$ and a collection of edges $E$ of $k$-element subsets of $V$ called hyperedges. The hypergraph vertex cover problem asks for a ...

Let us define the sketch as mapping $\varphi:R^D\to R^d$, such that for arbitrary $x\in\mathbb{R}^D$, its $\ell^1$ norm is preserved up to $\epsilon$ error, with $1-\delta$ success probability: $$\...

I am doing some research on machine learning algorithms in the context of a seminar, which focuses on Energy-Based Modeling vs Deep Learning specifically in working with images Modeling. Now I know ...

It occurred to me that if a given SAT is unsatisfiable, then a DPLL algorithm must try true/false settings for all literals to determine that there does not exist any satisfying literal combination. ...

The typical definition of dynamic transitive closure (or reachability) uses two types of queries: the first one is an update (edge deletion/insertion) and the second one is a reachability query. Thus, ...

I was wondering if there are any results that say how hard it is to answer the question are there TWO subsets that sum to a fixed value? In other words, the subset sum problem but asking if there are ...

Right now I am trying to understand the concept of simulation in theoretical computer science, focussing on Universal Turing machines. All textbooks that I looked into only explain examples. They ...

Assume that $\mathcal{A} = (Q_A, \Sigma, \Delta_A, q_{i_A}, F_A)$ and $\mathcal{B} = (Q_B, \Sigma, \Delta_B, q_{i_B}, F_B)$ are two NFAs. What is the worst-case time complexity of computing $\mathcal{...

(This question also suits for other similar natural $\mathrm{NP}$-hard problems) I know that there is a $4k^2$ vertex kernel (and $8k^2$ edge kernel) by Thomasse [Thomasse09] for Feedback Vertex Set (...

Underlying motivation for the question: if someone showed that $\text{P}=\text{NP}$ but the algorithm thus produced for, e.g., $3\text{-SAT}$, runs in time $\Omega(n^G)$ where $G$ is Graham's number, ...

I am working on an efficient pattern-matching algorithm (using binary files as input) based on suffix arrays. I would like to ask you If you are familiar with any suffix array construction algorithm (...

After quantum error correction was introduced in mid '90s, in subsequent years many of the classical analogues regarding the structure of code (such as singleton bound, GV bound etc) were obtained in ...

As the title says, I want to know when the treewidth of a bipartite graph is bounded by a constant. What families of graphs are both bipartite and bounded treewidth? More generally, I would like to ...

I'm looking at the nested positivity conditions for inductive types stated in the Coq manual. First off, are there any other references (not necessarily for Coq, but in dependent type theories ...

I have a seemingly simple task that I want to solve using an online algorithm but unfortunately I wasn't able to find relevant resources even though it seems so basic. The inputs are $D=(d_1,\dots,d_m)...

When I was a student, I was explained a problem that fascinated me, and at this time, I was told it's an NP-complete problem - which I ended up reducing to a combinatory problem according to notes I ...

Suppose I have a facility location problem with all service costs 0 (or infinity (in particular service costs are not metric)) such that the edges $ij$ for which facility $i$ can service client $j$ ...

I will be taking complexity class next quarter and we will use the book "B. Barak, S. Arora, Computational Complexity: A Modern Approach". However, I have little exposure to complexity ...

We say that a pair $(P,N)$ of subsets of strings from $\{0,1\}^n$ is an $n$-pair if $|P|=|N|=n$. Intuitively, sucha a pair consists of a set $P$ with $n$ positive $n$-bit strings, and a set $N$ with $...

Are there any standard recent survey articles on quantum error correction (and may be including fault Tolerant computing)? The most standard ones that many people refer to are this and this. Both of ...

Recently I became interested in grammar complexity of regular language. Prior to searching for literature, I tried to investigate it on my own, proving two lemmas from comment below. I am aware of an ...

I want to use use Agda to help me write proofs, but I am getting contradictory feedback about the value of proof relevance. Jacques Carette wrote a Proof-relevant Category Theory in Agda library. But ...

Let $\mathrm{GT}_n:\{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ be the greater than function: $\mathrm{GT}_n(x,y)=1$ exactly when the positive integer whose binary representation is $x$ is greater than the ...

I am completely new to information theory. I was learning about information content but couldn’t make sense of why the relationship between information content and probability isn’t linear? And why it ...

Is there is a subclass of regular graphs (say 4-regular graphs) for which there is a polynomial time algorithm to list all Eulerian orienations? An Eulerian orientaiton of an (undirected simple) graph ...

Given a graph $G=(V,E)$, a clique edge cover is a collection $C$ of subsets of $V$ such that each element $c$ of $C$ is a clique ($c \times c \subseteq E$) and $G$ is the union of these cliques ($E = \...

Q: Is there an efficient (I)LP formulation of planarity? More specifically, I am looking for a set of constraints that are satisfied by exactly all planar graphs on $n$ vertices, in order to optimize ...

Can someone provide a concise explanation of Minimap2 algorithm on how it is used in pairwise alignment? Here is the paper: https://academic.oup.com/bioinformatics/article/34/18/3094/4994778?login=...

Can someone recommend a reference on graph minors structure theorem and sublinear treewidth? Doesn't have to be the newest/strongest results as long as it's easier than tracking down all the papers ...

It is well-known that polynomial diophantine equations are undecidable (Hilbert's 10th problem): that is, given a quantifier-free formula over the language $\{=, +, \cdot, 1\}$ (of equality, addition, ...

In the dragon book 4.3.5 Non-Context-Free Language Constructs A few syntactic constructs found in typical programming languages cannot be speci ed using grammars alone. Here, we consider two of these ...

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